# American Institute of Mathematical Sciences

October  2015, 11(4): 1175-1183. doi: 10.3934/jimo.2015.11.1175

## The inventory model under supplier's partial trade credit policy in a supply chain system

 1 College of Business, Chung Yuan Christian University, Chung Li, Taiwan 2 Department of International Business Management, Shih Chien University, Taipei, Taiwan

Received  May 2014 Revised  August 2014 Published  March 2015

A lot of researchers explore the inventory EOQ model under the assumption that the supplier would offer the retailer full trade credit but not partial trade credit. In practice, the supplier's partial trade credit policy is frequently adopted in business transactions. This paper incorporates a real payment mode in which the retailers could still gradually settle the partial payment in the inventory EOQ model under the supplier's partial trade credit. Some theorems for the optimal cycle time are also proposed.
Citation: Kun-Jen Chung, Pin-Shou Ting. The inventory model under supplier's partial trade credit policy in a supply chain system. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1175-1183. doi: 10.3934/jimo.2015.11.1175
##### References:
 [1] M. Avriel, Nonlinear Programming: Analysis and Methods,, $1^{th}$ edition, (1976).   Google Scholar [2] K. J. Chung, A theorem on the determination of economic order quantity under conditions of permissible delay in payments,, Computers and Operations Research, 25 (1998), 49.  doi: 10.1016/S0305-0548(97)00041-5.  Google Scholar [3] K. J. Chung, Comments on the EOQ model under retailer partial trade credit policy in the supply chain,, International Journal of Production Economics, 114 (2008), 308.  doi: 10.1016/j.ijpe.2008.02.010.  Google Scholar [4] K. J. Chung, A complete proof on the solution procedure for non-instantaneous deteriorating items with permissible delay in payments,, Computers and Industrial Engineering, 56 (2009), 267.  doi: 10.1016/j.cie.2008.05.015.  Google Scholar [5] K. J. Chung, Using the convexities of total annual relevant costs to determine the optimal cycle times of inventory models for deteriorating items with permissible delay in payments,, Computers and Industrial Engineering, 58 (2010), 801.  doi: 10.1016/j.cie.2009.10.008.  Google Scholar [6] K. J. Chung, The complete proof on the optimal ordering policy under cash discount and trade credit,, International Journal of Systems Science, 41 (2010), 467.  doi: 10.1080/00207720903045866.  Google Scholar [7] K. J. Chung, Some improved algorithm to locate the optimal solutions for exponential deteriorating items under trade credit financing in a supply chain system,, Computers and Mathematics with Applications, 61 (2011), 2353.  doi: 10.1016/j.camwa.2010.12.054.  Google Scholar [8] K. J. Chung, The EOQ model with defective items and partially permissible delay in payments linked to order quantity derived analytically in the supply chain management,, Applied Mathematical Modelling, 37 (2013), 2317.  doi: 10.1016/j.apm.2012.05.014.  Google Scholar [9] K. J. Chung and H. F. Huang, The optimal cycle time for EPQ inventory model under permissible delay in payments,, International Journal of Production Economics , 84 (2003), 307.  doi: 10.1016/S0925-5273(02)00465-6.  Google Scholar [10] K. J. Chung and T. S. Huang, The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing,, International Journal of Production Economics, 106 (2007), 127.  doi: 10.1016/j.ijpe.2006.05.008.  Google Scholar [11] K. J. Chung and S. D. Lin, Some comments on retailer's inventory model under supplier's partial trade credit policy,, Journal of Information and Optimization Sciences, 30 (2009), 367.  doi: 10.1080/02522667.2009.10699883.  Google Scholar [12] K. J. Chung and S. D. Lin, The inventory model for trade credit in economic ordering policies of deteriorating items in a supply chain system,, Applied Mathematical Modelling, 35 (2011), 3111.  doi: 10.1016/j.apm.2010.12.001.  Google Scholar [13] S. K. Goyal, Economic order quantity under conditions of permissible delay in payments,, Journal of the Operational Research Society, 36 (1985), 335.  doi: 10.2307/2582421.  Google Scholar [14] Y. F. Huang, Retailer's inventory policy under supplier's partial trade credit policy,, Journal of the Operations Research Society of Japan, 48 (2005), 173.   Google Scholar [15] Y. F. Huang, Economic order quantity under conditionally permissible delay in payments,, European Journal of Operational Research, 176 (2007), 911.  doi: 10.1016/j.ejor.2005.08.017.  Google Scholar [16] Y. F. Huang and K. J. Chung, Optimal replenishment and payment policies in the EOQ model under cash discount and trade credit,, Asia-Pacific Journal of Operational Research, 20 (2003), 177.   Google Scholar [17] Y. F. Huang and K. H. Hsu, An EOQ model under retailer partial trade credit policy in supply chain,, International Journal of Production Economics, 112 (2008), 655.  doi: 10.1016/j.ijpe.2007.05.014.  Google Scholar [18] G. C. Mahata, An EPQ-based inventory model for exponential deteriorating items under retailer partial trade credit policy in supply chain,, Expert Systems with Applications, 39 (2012), 3537.  doi: 10.1016/j.eswa.2011.09.044.  Google Scholar [19] G. C. Mahata and P. Mahata, Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain,, Mathematical and Computer Modelling, 53 (2011), 1621.  doi: 10.1016/j.mcm.2010.12.028.  Google Scholar [20] J. T. Teng, On the economic order quantity under conditions of permissible delay in payments,, Journal of the Operational Research Society, 53 (2002), 915.  doi: 10.1057/palgrave.jors.2601410.  Google Scholar [21] J. T. Teng, Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers,, International Journal of Production Economics, 119 (2009), 415.  doi: 10.1016/j.ijpe.2009.04.004.  Google Scholar [22] J. T. Teng and S. K. Goyal, Optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credits,, Journal of the Operational Research Society, 58 (2007), 1252.  doi: 10.1057/palgrave.jors.2602404.  Google Scholar [23] A. Thangam and R. Uthayakumar, Optimal pricing and lot-sizing policy for a two-warehouse supply chain system with perishable items under partial credit financing,, Operational Research-International Journal, 10 (2010), 133.  doi: 10.1007/s12351-009-0066-2.  Google Scholar [24] G. F. Yen, K. J. Chung and T. C. Chen, The optimal retailer's ordering policies with trade credit financing and limited storage capacity in the supply chain system,, International Journal of Systems Science, 43 (2012), 2144.  doi: 10.1080/00207721.2011.565133.  Google Scholar

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##### References:
 [1] M. Avriel, Nonlinear Programming: Analysis and Methods,, $1^{th}$ edition, (1976).   Google Scholar [2] K. J. Chung, A theorem on the determination of economic order quantity under conditions of permissible delay in payments,, Computers and Operations Research, 25 (1998), 49.  doi: 10.1016/S0305-0548(97)00041-5.  Google Scholar [3] K. J. Chung, Comments on the EOQ model under retailer partial trade credit policy in the supply chain,, International Journal of Production Economics, 114 (2008), 308.  doi: 10.1016/j.ijpe.2008.02.010.  Google Scholar [4] K. J. Chung, A complete proof on the solution procedure for non-instantaneous deteriorating items with permissible delay in payments,, Computers and Industrial Engineering, 56 (2009), 267.  doi: 10.1016/j.cie.2008.05.015.  Google Scholar [5] K. J. Chung, Using the convexities of total annual relevant costs to determine the optimal cycle times of inventory models for deteriorating items with permissible delay in payments,, Computers and Industrial Engineering, 58 (2010), 801.  doi: 10.1016/j.cie.2009.10.008.  Google Scholar [6] K. J. Chung, The complete proof on the optimal ordering policy under cash discount and trade credit,, International Journal of Systems Science, 41 (2010), 467.  doi: 10.1080/00207720903045866.  Google Scholar [7] K. J. Chung, Some improved algorithm to locate the optimal solutions for exponential deteriorating items under trade credit financing in a supply chain system,, Computers and Mathematics with Applications, 61 (2011), 2353.  doi: 10.1016/j.camwa.2010.12.054.  Google Scholar [8] K. J. Chung, The EOQ model with defective items and partially permissible delay in payments linked to order quantity derived analytically in the supply chain management,, Applied Mathematical Modelling, 37 (2013), 2317.  doi: 10.1016/j.apm.2012.05.014.  Google Scholar [9] K. J. Chung and H. F. Huang, The optimal cycle time for EPQ inventory model under permissible delay in payments,, International Journal of Production Economics , 84 (2003), 307.  doi: 10.1016/S0925-5273(02)00465-6.  Google Scholar [10] K. J. Chung and T. S. Huang, The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing,, International Journal of Production Economics, 106 (2007), 127.  doi: 10.1016/j.ijpe.2006.05.008.  Google Scholar [11] K. J. Chung and S. D. Lin, Some comments on retailer's inventory model under supplier's partial trade credit policy,, Journal of Information and Optimization Sciences, 30 (2009), 367.  doi: 10.1080/02522667.2009.10699883.  Google Scholar [12] K. J. Chung and S. D. Lin, The inventory model for trade credit in economic ordering policies of deteriorating items in a supply chain system,, Applied Mathematical Modelling, 35 (2011), 3111.  doi: 10.1016/j.apm.2010.12.001.  Google Scholar [13] S. K. Goyal, Economic order quantity under conditions of permissible delay in payments,, Journal of the Operational Research Society, 36 (1985), 335.  doi: 10.2307/2582421.  Google Scholar [14] Y. F. Huang, Retailer's inventory policy under supplier's partial trade credit policy,, Journal of the Operations Research Society of Japan, 48 (2005), 173.   Google Scholar [15] Y. F. Huang, Economic order quantity under conditionally permissible delay in payments,, European Journal of Operational Research, 176 (2007), 911.  doi: 10.1016/j.ejor.2005.08.017.  Google Scholar [16] Y. F. Huang and K. J. Chung, Optimal replenishment and payment policies in the EOQ model under cash discount and trade credit,, Asia-Pacific Journal of Operational Research, 20 (2003), 177.   Google Scholar [17] Y. F. Huang and K. H. Hsu, An EOQ model under retailer partial trade credit policy in supply chain,, International Journal of Production Economics, 112 (2008), 655.  doi: 10.1016/j.ijpe.2007.05.014.  Google Scholar [18] G. C. Mahata, An EPQ-based inventory model for exponential deteriorating items under retailer partial trade credit policy in supply chain,, Expert Systems with Applications, 39 (2012), 3537.  doi: 10.1016/j.eswa.2011.09.044.  Google Scholar [19] G. C. Mahata and P. Mahata, Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain,, Mathematical and Computer Modelling, 53 (2011), 1621.  doi: 10.1016/j.mcm.2010.12.028.  Google Scholar [20] J. T. Teng, On the economic order quantity under conditions of permissible delay in payments,, Journal of the Operational Research Society, 53 (2002), 915.  doi: 10.1057/palgrave.jors.2601410.  Google Scholar [21] J. T. Teng, Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers,, International Journal of Production Economics, 119 (2009), 415.  doi: 10.1016/j.ijpe.2009.04.004.  Google Scholar [22] J. T. Teng and S. K. Goyal, Optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credits,, Journal of the Operational Research Society, 58 (2007), 1252.  doi: 10.1057/palgrave.jors.2602404.  Google Scholar [23] A. Thangam and R. Uthayakumar, Optimal pricing and lot-sizing policy for a two-warehouse supply chain system with perishable items under partial credit financing,, Operational Research-International Journal, 10 (2010), 133.  doi: 10.1007/s12351-009-0066-2.  Google Scholar [24] G. F. Yen, K. J. Chung and T. C. Chen, The optimal retailer's ordering policies with trade credit financing and limited storage capacity in the supply chain system,, International Journal of Systems Science, 43 (2012), 2144.  doi: 10.1080/00207721.2011.565133.  Google Scholar
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